Lee, Conditional edge-fault Hamiltonicity of matching composition networks, IEEE Trans. Chen, Pancyclicity in Möbius cubes with maximal edge faults, Parallel Comput., 30 ( 2004), pp. ITCOB4 0018-9340 Crossref ISI Google Scholar Chang, Hamiltonian path embedding and pancyclicity on the Möbius cube with faulty nodes and faulty edges, IEEE Trans. JOSUED 0920-8542 Crossref ISI Google Scholar Chen, Embedding fault-free cycles in crossed cubes with conditional link faults, J. TCSCDI 0304-3975 Crossref ISI Google Scholar Fu, Fault-free Hamiltonian cycles in twisted cubes with conditional link faults, Theoret. ITDSEO 1045-9219 Crossref ISI Google Scholar Efe, The crossed cube architecture for parallel computation, IEEE Trans. IFPLAT 0020-0190 Crossref ISI Google Scholar Chedid, On the generalized twisted cube, Inform. Lee, On the existence of Hamiltonian circuits in faulty hypercubes, SIAM J. JGTHDO 0364-9024 Crossref ISI Google Scholar Tindell, Circulants and their connectivities, J. Stewart, Fault-tolerant embeddings of Hamiltonian circuits in k-ary n-cubes, SIAM J. We also show that if the base network is hamiltonian connected, RDNk (B) is hamiltonian connected for any k > 0.Y. We give an efficient algorithm for constructing a hamiltonian cycle in RDNk (B) for k > 0. In this paper, we show that, if the base network B is hamiltonian, RDNk (B) is hamiltonian. Therefore, a k-level Recursive Dual-Net RDNk (B) contains (2n0)2k/2 nodes with a node degree of d0 + k, where n0 and d0 are the size and the node-degree of the base network B, respectively. node-degree d + 1, where n and d are the size and the node-degree of G, respectively. The dual-construction extends a symmetric graph G into a symmetric graph G' with size 2n2 and. At each iteration, the network is extended through dual-construction.

A Recursive Dual-Net RDN (B) is recursively constructed on a base symmetric network B. Recursive Dual-Net (RDN) was proposed recently as an effective, high-performance interconnection network for supercomputers with millions of nodes. My own experience from teaching out of the subject more than ten years at University of Science and Technology of China (USTC) shows that this treatment makes hardly the course di:fficult, but much more accords with the essence and the development trend of the subject. The method we deal with the mate rials is to particularly lay stress on digraphs, regarding undirected graphs as their special cases. All materials presented in this book, however, I believe, are the most classical, fundamental, interesting and important. The richness of theory and the wideness of applications make it impossi ble to include all topics in graph theory in a textbook for one semester. This book provides an introduction to graph theory for these students. More and more colleges and universities have made it a required course for the senior or the beginning postgraduate students who are majoring in mathematics, computer science, electronics, scientific management and others. In recent three decades the exciting and rapidly growing area of the subject abounds with new mathematical devel opments and significant applications to real-world problems. In the spectrum of mathematics, graph theory which studies a mathe matical structure on a set of elements with a binary relation, as a recognized discipline, is a relative newcomer.

Hypercube in mathematica